On smooth lattice polytopes with small degree

TL;DR

This paper classifies smooth lattice polytopes with small degree by linking their properties to polarized toric varieties using tools from Adjunction and Mori theories.

Contribution

It extends previous classifications by interpreting polytope degree as a geometric invariant within the toric variety framework.

Findings

Classification of smooth lattice polytopes with small degree

Application of Adjunction and Mori theories to polytope analysis

Extension of prior classification results

Abstract

Toric geometry provides a bridge between the theory of polytopes and algebraic geometry: one can associate to each lattice polytope a polarized toric variety. In this paper we explore this correspondence to classify smooth lattice polytopes having small degree, extending a classification provided by Dickenstein, Di Rocco and Piene. Our approach consists in interpreting the degree of a polytope as a geometric invariant of the corresponding polarized variety, and then applying techniques from Adjunction Theory and Mori Theory.